Axiom:Axiom of Pairing/Set Theory/Strong Form

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For any two sets, there exists a set to which only those two sets are elements:

$\forall a: \forall b: \exists c: \forall z: \paren {z = a \lor z = b \iff z \in c}$

That is, let $a$ and $b$ be sets.

Then there exists a set $c$ such that $c = \set {a, b}$.

Thus it is possible to create a set whose elements are two sets that have already been created.

Also known as

The axiom of pairing is also known as the axiom of the unordered pair.

Some sources call it the pairing axiom.

Also see